2,798 research outputs found
Application of p-adic analysis to models of spontaneous breaking of the replica symmetry
Methods of p-adic analysis are applied to the investigation of the
spontaneous symmetry breaking in the models of spin glasses. A p-adic
expression for the replica matrix is given and moreover the replica matrix in
the models of spontaneous breaking of the replica symmetry in the simplest case
is expressed in the form of the Vladimirov operator of p-adic fractional
differentiation. Also the model of hierarchical diffusion (that was proposed to
describe relaxation of spin glasses) investigated using p-adic analysis.Comment: Latex, 8 page
Lifelong Learning of Spatiotemporal Representations with Dual-Memory Recurrent Self-Organization
Artificial autonomous agents and robots interacting in complex environments
are required to continually acquire and fine-tune knowledge over sustained
periods of time. The ability to learn from continuous streams of information is
referred to as lifelong learning and represents a long-standing challenge for
neural network models due to catastrophic forgetting. Computational models of
lifelong learning typically alleviate catastrophic forgetting in experimental
scenarios with given datasets of static images and limited complexity, thereby
differing significantly from the conditions artificial agents are exposed to.
In more natural settings, sequential information may become progressively
available over time and access to previous experience may be restricted. In
this paper, we propose a dual-memory self-organizing architecture for lifelong
learning scenarios. The architecture comprises two growing recurrent networks
with the complementary tasks of learning object instances (episodic memory) and
categories (semantic memory). Both growing networks can expand in response to
novel sensory experience: the episodic memory learns fine-grained
spatiotemporal representations of object instances in an unsupervised fashion
while the semantic memory uses task-relevant signals to regulate structural
plasticity levels and develop more compact representations from episodic
experience. For the consolidation of knowledge in the absence of external
sensory input, the episodic memory periodically replays trajectories of neural
reactivations. We evaluate the proposed model on the CORe50 benchmark dataset
for continuous object recognition, showing that we significantly outperform
current methods of lifelong learning in three different incremental learning
scenario
Analysis of the infinity-replica symmetry breaking solution of the Sherrington-Kirkpatrick model
In this work we analyse the Parisi's infinity-replica symmetry breaking
solution of the Sherrington - Kirkpatrick model without external field using
high order perturbative expansions. The predictions are compared with those
obtained from the numerical solution of the infinity-replica symmetry breaking
equations which are solved using a new pseudo-spectral code which allows for
very accurate results. With this methods we are able to get more insight into
the analytical properties of the solutions. We are also able to determine
numerically the end-point x_{max} of the plateau of q(x) and find that lim_{T
--> 0} x_{max}(T) > 0.5.Comment: 15 pages, 11 figures, RevTeX 4.
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